Following the same computations as in Lemma 8 of [1]}, it holds that
\( \left| Q \right|& \le C_{\eta } \left(\phi ^{2} + \zeta ^{2}\right) \left(\Theta _{x}^{2} + \left|\Theta ^{c}_{x x}\right|\right) + \eta \zeta _{x}^{2} + C \delta \mathrm {e}^{-c_{0}(|x|+t)} \nonumber \\[3mm]& \le C_{\eta } \left(\phi ^{2} + \zeta ^{2}\right) \left(\delta ^{\frac{1}{4}}(1+t)^{-\frac{7}{4}} + \delta (1+t)^{-1} \mathrm {e}^{ -\frac{\hat{c} x^{2}}{1+t} } \right) + \eta \zeta _{x}^{2} + C \delta \mathrm {e}^{-c_{0}(|x|+t)}, \) 
